Question

The angle of elevation from a park bench 724 feet from the base of the Gateway Arch in St. Louis, Missouri is 22°. How tall is the Gateway Arch, rounded to the nearest whole number?

Answer 1

Gateway Arch is
`292.46` feet tall

Explanation:

As we know,

the horizontal distance from the gate of the Arch to the bench
`= 724` feet

The angle of elevation is
`22` degree

Let H be the height of the gate be "H"

Tanθ= Perpendicular/Base

Substituting the given values in above equation, we get -

`tan 22 = (H)/(724) \\H = 724 * tan 22\\H = 724 * 0.404\\H = 292.46`feet